{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TJ4PZABWS75J5HHAW324X6YEAD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8651bab0ad1efd3caba852f700e65194b66c823243759c8a6f9eed790d610fbc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T07:56:46Z","title_canon_sha256":"8d40bc633a438e0db8fa1ee61ea34c5b9a2b8cdebf504122cb540f55c04c5b63"},"schema_version":"1.0","source":{"id":"2607.07115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07115","created_at":"2026-07-09T01:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07115v1","created_at":"2026-07-09T01:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07115","created_at":"2026-07-09T01:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"TJ4PZABWS75J","created_at":"2026-07-09T01:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"TJ4PZABWS75J5HHA","created_at":"2026-07-09T01:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"TJ4PZABW","created_at":"2026-07-09T01:20:14Z"}],"graph_snapshots":[{"event_id":"sha256:dd48060bb567c28cc5f2cb3d671564c492e2fb22a6433e0f4a3ed1ce2cd3abbf","target":"graph","created_at":"2026-07-09T01:20:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.07115/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the one-dimensional Gross-Pitaevskii equation with a traveling delta potential and non-zero conditions at infinity. This model describes the effect of a moving impurity in a quantum fluid. Firstly, we show that the associated Cauchy problem is globally well-posed in the energy space. This requires the definition of a conserved energy, which involves the notion of renormalized momentum. Secondly, we study the existence and stability of stationary states in a co-moving reference frame. It is known that there exists an impurity-dependent critical velocity above which no stationary state ","authors_text":"Martino Caliaro, Paolo Antonelli","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T07:56:46Z","title":"On the Gross-Pitaevskii model with a moving impurity: Cauchy problem and superfluidity criterion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07115","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bb2369bab969cd3c738d546d5db6f92a86158f7f5be9db67080bf869b1d31537","target":"record","created_at":"2026-07-09T01:20:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8651bab0ad1efd3caba852f700e65194b66c823243759c8a6f9eed790d610fbc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T07:56:46Z","title_canon_sha256":"8d40bc633a438e0db8fa1ee61ea34c5b9a2b8cdebf504122cb540f55c04c5b63"},"schema_version":"1.0","source":{"id":"2607.07115","kind":"arxiv","version":1}},"canonical_sha256":"9a78fc803697fa9e9ce0b6f5cbfb0400fd613c18cb4e51052948a436423d09c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a78fc803697fa9e9ce0b6f5cbfb0400fd613c18cb4e51052948a436423d09c0","first_computed_at":"2026-07-09T01:20:14.852364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:14.852364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5sYq05lPHZBFLFaXSzy6+cEfB4d5KftXGJ/IelqUMMMpjH3aHfx9aV7vCCoRhvA1w/jWObpuYA7GoIXvK01DQ==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:14.852864Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb2369bab969cd3c738d546d5db6f92a86158f7f5be9db67080bf869b1d31537","sha256:dd48060bb567c28cc5f2cb3d671564c492e2fb22a6433e0f4a3ed1ce2cd3abbf"],"state_sha256":"ff431a792f4a5c0c9d47e3ed1dddd388918b1715c794645abb21006d0545d008"}